While setting up virtual connections in an ATM switching network operating according to an asynchronous transfer mode, separate path finding occurs within individual ATM switching equipment respectively, such that a suitable path for a virtual connection across the switching network belonging to the ATM switching equipment, can be defined. Given a multi-stage switching network having individual switching elements connected together by internal ATM links, such separate path finding occurs based on both the bit rate reported for the respective virtual connection, and the remaining bit rate transmission capacities that are momentarily available on the individual ATM links.
In addition to finding such an internal path within the ATM switching device, one of the individual ATM trunks of the ATM trunk group being considered must also be selected for a virtual connection to be set up when not only individual ATM trunk, but also external ATM trunk groups, formed of a plurality of individual ATM trunks, are provided within an ATM switching network between ATM communication devices. An individual ATM trunk is selected before finding the internal path within the respective ATM switching device.